While working for diamond camo on special weapons, I've found that the crossbow is very buggy with tracking challenges. Cherry Blossom, Art of War, Carbon Fiber, and Ronin all don't track correctly and are basically currently unobtainable through legitimate means.
Also, I can't supply actual number results but it definitely seems that the crossbow kills in general aren't tracked consistently, every 10 kills would award about 7 kills of progress towards the challenges.